Once or twice in a decade, a Broadway show comes along that is so innovative and unprecedented that it changes the American musical theater as we know it. In the 1990s, it was Rent. Nearly five years ago, it was the irreverent The Book of Mormon. In 2015, the game-changing musical is, without question, the blockbuster Hamilton, which recently transferred to Broadway after a sold-out run downtown at the Public Theater.

Indeed, Alexander Hamilton is mostly known to Americans for being on the $10 bill because he was one of the founding fathers of the United States. Unless one is an American history buff, we forget that Hamilton was chief state aide to George Washington, advocate of the U.S. Constitution, founder of the U.S. financial system, the first Secretary of the Treasury, and founder of the world’s first voter-based political system, the Federalist Party, and more. Most know the stories of the other founding fathers of our nation, but not Hamilton, and the true genius of this show is how music, lyric and book writer Lin-Manuel Miranda used Ron Chernow’s biography of Hamilton as the basis for the story and created a theatrical masterpiece. Mr. Miranda has taken what’s normally considered a dry subject, early American history, and turned it into an entertaining epic that appeals to the masses of all ages. Yes, the chronology of events in the American Revolutionary War are all here, but Mr. Miranda adds depth and complexity to everyone from George Washington (Christopher Jackson) to Aaron Burr (Leslie Odom, Jr.) and Thomas Jefferson (Daveed Diggs). There hasn’t been a Broadway musical with this much youthful magnetism and solid storytelling in many moons.

Hype has surrounded this show ever since it debuted at the Public this past winter. Hamilton has been the hottest ticket in town and one has not been able to go online or open a newspaper or magazine without reading some blurb singing its praises in the past six months. The hoopla is all justified, because from the two opening numbers, “Alexander Hamilton” (an expository song that sums up the man’s early life) and “My Shot” in Act I, Hamilton at first seems more like a seamless, energetic pop music concert than a Broadway musical, but in essence there is really nothing gimmicky going on at all. Yes, there are hip-hop and pop-style songs, but also many beautiful ballads and more traditional show tunes, all of which propel the story forward exquisitely. Mr. Miranda has also created an intricate historical epic that unfolds with rapid-fire energy and never lets up. It is completely unlike any of Mr. Miranda’s previous efforts, namely In the Heights, which won the Tony Award for Best Musical in 2008.

We learn all the biographical details about Alexander Hamilton, the illegitimate son of a Scotsman and a prostitute born in the Caribbean, to his journey to America and how he helped the other founding fathers create the new USA after the Revolutionary War, but we also learn about Hamilton’s clashes with the third Vice President of the United States, Aaron Burr (Mr. Odom, Jr.), in the show-stopping song “The Room Where It Happens,” a number so infectious that it could easily be released as a pop song on the radio. The same holds true for George Washington’s ballad “One Last Time.” As Hamilton, Mr. Miranda’s performance is consistently solid, sincere and convincing, even if he’s not always the most dynamic performer on the stage.

Stage and TV star Jonathan Groff is a true scene-stealer as Mad King George III, America’s last monarch. Taking over the role originated Off Broadway at the Public by Brian d’Arcy James, Mr. Groff, clad in his huge regal crown and full king regalia, holding an imperial scepter, portrays the king as a petulant buffoon, seeing the revolting colonists as naughty, wayward children as he belts out such songs as “You’ll Be Back” with amusing, snarky aplomb.

The women in Hamilton’s life are just as influential, showing how they, too, made a difference in the early days of our nation. Renee Elise Goldsberry, as Angelica Schuyler, the sister of Hamilton’s wife, is especially moving whenever she sings “Satisfied” in her soaring voice. Phillipa Soo is equally outstanding as Eliza, Hamilton’s wife, a woman who petitioned Congress to publish her husband’s writings. Whenever Ms. Goldsberry and Ms. Soo sing, they bring down the proverbial house. Ms. Soo is absolutely haunting when singing “Burn,” a ballad about the pain of being Hamilton’s long-suffering wife.

Director Thomas Kail keeps the story moving along with fluid precision and at an exhausting, nonstop pace at all times. Andy Blankenbuehler’s choreography is graceful and marvelously stylized; the fusion of direction and choreography complement each other in the frenetic goings-on in this nearly three-hour, monumental show. Hamilton has truly started a Broadway revolution and will continue to influence the American musical theater for years to come.